lib/round.c

   1 /* Round toward nearest, breaking ties away from zero.
   2    Copyright (C) 2007, 2010-2011 Free Software Foundation, Inc.
   3
   4    This program is free software; you can redistribute it and/or modify
   5    it under the terms of the GNU Lesser General Public License as published by
   6    the Free Software Foundation; either version 2, or (at your option)
   7    any later version.
   8
   9    This program is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12    GNU Lesser General Public License for more details.
  13
  14    You should have received a copy of the GNU Lesser General Public License along
  15    with this program; if not, write to the Free Software Foundation,
  16    Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.  */
  17
  18 /* Written by Ben Pfaff <blp@gnu.org>, 2007.
  19    Based heavily on code by Bruno Haible. */
  20
  21 #include <config.h>
  22
  23 /* Specification.  */
  24 #include <math.h>
  25
  26 #include <float.h>
  27
  28 #undef MIN
  29
  30 #ifdef USE_LONG_DOUBLE
  31 # define ROUND roundl
  32 # define FLOOR floorl
  33 # define CEIL ceill
  34 # define DOUBLE long double
  35 # define MANT_DIG LDBL_MANT_DIG
  36 # define MIN LDBL_MIN
  37 # define L_(literal) literal##L
  38 # define HAVE_FLOOR_AND_CEIL HAVE_FLOORL_AND_CEILL
  39 #elif ! defined USE_FLOAT
  40 # define ROUND round
  41 # define FLOOR floor
  42 # define CEIL ceil
  43 # define DOUBLE double
  44 # define MANT_DIG DBL_MANT_DIG
  45 # define MIN DBL_MIN
  46 # define L_(literal) literal
  47 # define HAVE_FLOOR_AND_CEIL 1
  48 #else /* defined USE_FLOAT */
  49 # define ROUND roundf
  50 # define FLOOR floorf
  51 # define CEIL ceilf
  52 # define DOUBLE float
  53 # define MANT_DIG FLT_MANT_DIG
  54 # define MIN FLT_MIN
  55 # define L_(literal) literal##f
  56 # define HAVE_FLOOR_AND_CEIL HAVE_FLOORF_AND_CEILF
  57 #endif
  58
  59 /* -0.0.  See minus-zero.h.  */
  60 #if defined __hpux || defined __sgi || defined __ICC
  61 # define MINUS_ZERO (-MIN * MIN)
  62 #else
  63 # define MINUS_ZERO L_(-0.0)
  64 #endif
  65
  66 /* If we're being included from test-round2[f].c, it already defined names for
  67    our round implementations.  Otherwise, pick the preferred implementation for
  68    this machine. */
  69 #if !defined FLOOR_BASED_ROUND && !defined FLOOR_FREE_ROUND
  70 # if HAVE_FLOOR_AND_CEIL
  71 #  define FLOOR_BASED_ROUND ROUND
  72 # else
  73 #  define FLOOR_FREE_ROUND ROUND
  74 # endif
  75 #endif
  76
  77 #ifdef FLOOR_BASED_ROUND
  78 /* An implementation of the C99 round function based on floor and ceil.  We use
  79    this when floor and ceil are available, on the assumption that they are
  80    faster than the open-coded versions below. */
  81 DOUBLE
  82 FLOOR_BASED_ROUND (DOUBLE x)
  83 {
  84   if (x >= L_(0.0))
  85     {
  86       DOUBLE y = FLOOR (x);
  87       if (x - y >= L_(0.5))
  88         y += L_(1.0);
  89       return y;
  90     }
  91   else
  92     {
  93       DOUBLE y = CEIL (x);
  94       if (y - x >= L_(0.5))
  95         y -= L_(1.0);
  96       return y;
  97     }
  98 }
  99 #endif /* FLOOR_BASED_ROUND */
 100
 101 #ifdef FLOOR_FREE_ROUND
 102 /* An implementation of the C99 round function without floor or ceil.
 103    We use this when floor or ceil is missing. */
 104 DOUBLE
 105 FLOOR_FREE_ROUND (DOUBLE x)
 106 {
 107   /* 2^(MANT_DIG-1).  */
 108   static const DOUBLE TWO_MANT_DIG =
 109     /* Assume MANT_DIG <= 5 * 31.
 110        Use the identity
 111        n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
 112     (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
 113     * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
 114     * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
 115     * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
 116     * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
 117
 118   /* The use of 'volatile' guarantees that excess precision bits are dropped at
 119      each addition step and before the following comparison at the caller's
 120      site.  It is necessary on x86 systems where double-floats are not IEEE
 121      compliant by default, to avoid that the results become platform and
 122      compiler option dependent.  'volatile' is a portable alternative to gcc's
 123      -ffloat-store option.  */
 124   volatile DOUBLE y = x;
 125   volatile DOUBLE z = y;
 126
 127   if (z > L_(0.0))
 128     {
 129       /* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1).  */
 130       if (z < L_(0.5))
 131         z = L_(0.0);
 132       /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
 133       else if (z < TWO_MANT_DIG)
 134         {
 135           /* Add 0.5 to the absolute value.  */
 136           y = z += L_(0.5);
 137           /* Round to the next integer (nearest or up or down, doesn't
 138              matter).  */
 139           z += TWO_MANT_DIG;
 140           z -= TWO_MANT_DIG;
 141           /* Enforce rounding down.  */
 142           if (z > y)
 143             z -= L_(1.0);
 144         }
 145     }
 146   else if (z < L_(0.0))
 147     {
 148       /* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)).  */
 149       if (z > - L_(0.5))
 150         z = MINUS_ZERO;
 151       /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
 152       else if (z > -TWO_MANT_DIG)
 153         {
 154           /* Add 0.5 to the absolute value.  */
 155           y = z -= L_(0.5);
 156           /* Round to the next integer (nearest or up or down, doesn't
 157              matter).  */
 158           z -= TWO_MANT_DIG;
 159           z += TWO_MANT_DIG;
 160           /* Enforce rounding up.  */
 161           if (z < y)
 162             z += L_(1.0);
 163         }
 164     }
 165   return z;
 166 }
 167 #endif /* FLOOR_FREE_ROUND */
 168